It could be not that hard if it is only simple music..
(simple notes, no custom techniques).
First the AY frequency counter is 12-bit versus 10-bit on the PSG
which allows for a lower frequency range.
(ex: PSG lowest Tone FRQ possible = counter set to 1024 = 109.239044 Hz (NTSC clocked))
Secondly the AY might have a different Master Clock on the original system the music/Fx was made for.

Also,
the AY can mix its Noise channel with the Tone channels which PSG cannot.
The Noise frequency system on the AY is also different but lacks the wide frequency range the PSG has when controlled by its third tone channel...

Volume is the same , 4-bit, excepted that the AY has an optional hardware envelope mode...which is, by the way, the SSG part of the YM2612
If it is in use, you can sort of emulate this (because the volume is also 4-bit)
knowing that the envelope period is 16-bit,Envelope period frequency(Hz) = fMasterClock(hz)/256*(16-bit envelope period)
You also have to take in account the hardware envelope shape register, which will toggle the CONT, ATT, ALT and HOLD bits to form a looping (or not looping envelope) >>see the Nemesis SSG detail in the YM2612 sticky for further infos..

Last but not least, AY Music or (YM2149) might use custom techniques which will require a high resolution update rate, for example using the hardware looping envelope to produce saw tooth or triangle shaped bass notes, or Timer synced writes directly to the volume register to create modulation or custom waveforms at audio rates...

All of this can be emulated on the PSG (I did a lot of tests on hardware for my SPSG SN76489 VST) but some expansive things might not be easy with a game running at the same time